A General Construction of JSJ Decompositions

  • Vincent Guirardel
  • Gilbert Levitt
Part of the Trends in Mathematics book series (TM)


This is an extended and updated version of a talk given by Gilbert Levitt in Barcelona on July 2, 2005 about joint work with Vincent Guirardel, currently being written. It is based on notes TEX’d by Peter Kropholler. I thank Peter for making his notes available to me. Of course, he shouldn’t be held responsible for the content. Thanks also to the organizers of the Barcelona Conference on Geometric Group Theory, and to the referee for helpful suggestions.


Hyperbolic Group Deformation Space Vertex Group Quotient Graph Edge Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [Bo]
    B. Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998), 145–186.MATHCrossRefMathSciNetGoogle Scholar
  2. [Du]
    M.J. Dunwoody, Folding sequences, Geometry and Topology monographs 1 (1998), 139–158.MathSciNetCrossRefGoogle Scholar
  3. [DS]
    M.J. Dunwoody, M.E. Sageev, JSJ-splittings for finitely presented groups over slender groups, Invent. Math. 135 (1999), 25–44.MATHCrossRefMathSciNetGoogle Scholar
  4. [Fo 1]
    M. Forester, Deformation and rigidity of simplicial group actions on trees, Geom. & Topol. 6 (2002), 219–267.MATHCrossRefMathSciNetGoogle Scholar
  5. [Fo 2]
    M. Forester, On uniqueness of JSJ decompositions of finitely generated groups, Comm. Math. Helv. 78 (2003), 740–751.MATHCrossRefMathSciNetGoogle Scholar
  6. [Fo 3]
    M. Forester, Splittings of generalized Baumslag-Solitar groups, Geom. Dedicata 121 (2006), 43–59.MATHCrossRefMathSciNetGoogle Scholar
  7. [FP]
    K. Fujiwara, P. Papasoglu, JSJ-decompositions of finitely presented groups and complexes of groups GAFA 16 (2006), 70–125.MATHCrossRefMathSciNetGoogle Scholar
  8. [Gu]
    V. Guirardel, Reading small actions of a one-ended hyperbolic group on R-trees from its JSJ splitting, Am. J. Math. 122 (2000), 667–688.MATHCrossRefMathSciNetGoogle Scholar
  9. [GL]
    V. Guirardel, G. Levitt, Deformation spaces of trees, Groups, Geometry, and Dynamics 1 (2007), 135–181.MATHMathSciNetGoogle Scholar
  10. [Le]
    G. Levitt, Automorphisms of hyperbolic groups and graphs of groups, Geom. Dedic. 114 (2005), 49–70.MATHCrossRefMathSciNetGoogle Scholar
  11. [RS]
    E. Rips, Z. Sela, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Ann. Math. 146 (1997), 55–109.MATHMathSciNetCrossRefGoogle Scholar
  12. [SS]
    P. Scott, G.A. Swarup, Regular neighbourhoods and canonical decompositions for groups, Astérisque 289 (2003).Google Scholar
  13. [Vo]
    K. Vogtmann, Automorphisms of free groups and Outer space, Geom. Dedicata 94 (2002), 1–31.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Vincent Guirardel
    • 1
  • Gilbert Levitt
    • 2
  1. 1.Laboratoire Émile PicardUniversité Paul SabatierToulouse Cedex 4France
  2. 2.LMNOUniversité de CaenCaen CedexFrance

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